C ) can be made precise in several ways; the most succinct formulation uses the language of adjoint functors . Every functor F  : D ? E induces a f...

Diagonal functor : The diagonal functor is defined as the functor from D to the functor category D C which sends each object in D to the constant f...

Problems formulated with adjoint functors 1.3 Adjoint functors as solving optimization problems 1.4 The case of partial orders 2 Formal definitions...

It follows that any functor which preserves limits will take terminal objects to terminal objects, and any functor which preserves colimits will ta...

Functors Main article: functor Functors are structure-preserving maps between categories. They can be thought of as morphisms in the category of al...

Universal cones Limits and colimits are defined as universal cones . That is, cones through which all other cones factor. A cone ? from L to F is a...

In that case, homotopy defines an equivalence relation on the hom sets in the model category giving rise to homotopy classes. [ edit ] Characteriza...

Another article treats the concept of species in biology . In combinatorial mathematics , the theory of combinatorial species is an abstract, syste...

X i , f ij ) be a direct system of objects and morphisms in a category C (same definition as above). The direct limit of this system is an object X...